The Position of a Particle Is Given by the Function $2 t ^ { 3 } - 9 t ^ { 2 } + 12 t$

Essay

The position of a particle is given by the function s(t) = $2 t ^ { 3 } - 9 t ^ { 2 } + 12 t$ , where t is measured in seconds and s in meters.(a) Find the velocity at time t.(b) When is the particle at rest?
(c) When is the particle moving in the positive direction?
(d) Draw a diagram to represent the motion of the particle.(e) Find the total distance traveled by the particle during the time interval [1,3].